Subject

Mathematics

Class

CBSE Class 12

Pre Boards

Practice to excel and get familiar with the paper pattern and the type of questions. Check you answers with answer keys provided.

Sample Papers

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 Multiple Choice QuestionsShort Answer Type

11.

Find the angle between the vector straight i with hat on top minus straight j with hat on top space and space straight j with hat on top space minus space straight k with hat on top.

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12.

Find the distance of a point (2, 5, −3) from the plane straight r with rightwards arrow on top. open parentheses 6 straight i with hat on top minus 3 straight j with hat on top plus 2 straight k with hat on top close parentheses space equals 4.

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13.

Find the differential equation of the family of lines passing through the origin. 

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14.

Find the integrating factor for the following differential equation:straight x space log space straight x dy over dx space plus space straight y space equals space 2 logx space

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15.

Evaluate: integral subscript 0 superscript straight pi divided by 2 end superscript fraction numerator sin squared straight x over denominator sinx plus cosx end fraction dx.

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16.

Evaluate integral subscript negative 1 end subscript superscript 2 left parenthesis straight e to the power of 3 straight x end exponent plus 7 straight x minus 5 right parenthesis dx

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17.

Evaluate:
integral fraction numerator straight x squared over denominator straight x to the power of 4 plus straight x squared minus 2 end fraction dx

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18.

In a set of 10 coins, 2 coins are with heads on both the sides. A coin is selected at random from this set and tossed five times. If all the five times, the result was heads, find the probability that the selected coin had heads on both the sides

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19.

How many times must a fair coin be tossed so that the probability of getting at least one head is more than 80%?

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20.

Find x such that the four points A(4, 1, 2), B(5, x, 6) , C(5, 1, -1) and D(7, 4, 0) are coplanar.


Position space vector space of space OA with rightwards arrow on top space equals space 4 straight i with hat on top plus straight j with hat on top space plus space 2 straight k with hat on top
Position space vector space of space OB with rightwards arrow on top space equals space 5 straight i with hat on top plus straight x straight j with hat on top plus 6 straight k with hat on top
Position space vector space of space OD with rightwards arrow on top space equals 7 straight i with hat on top plus 4 straight j with hat on top plus 0 straight k with hat on top
AB with rightwards arrow on top space equals space OB with rightwards arrow on top space minus space OA with rightwards arrow on top
space space equals space 5 straight i with hat on top plus straight x straight j with hat on top plus 6 straight k with hat on top minus 4 straight i with hat on top minus straight j with hat on top minus 2 straight k with hat on top equals straight i with hat on top plus left parenthesis straight x minus 1 right parenthesis straight j with hat on top plus 4 straight k with hat on top
space space space space AC with rightwards arrow on top space equals space OC with rightwards arrow on top space minus space OA with rightwards arrow on top
space space space space space space equals 5 straight i with hat on top space plus straight j with hat on top minus straight k with hat on top space minus 4 straight i with hat on top minus straight j with hat on top minus 2 straight k with hat on top space equals space straight i with hat on top minus 3 straight k with hat on top
space space space space space space AD with rightwards arrow on top space equals space OD with rightwards arrow on top space minus space OA with rightwards arrow on top
space space space space space space space space equals 7 straight i with hat on top plus 4 straight j with hat on top plus 0 straight k with hat on top minus 4 straight i with hat on top minus straight j with hat on top minus 2 straight k with hat on top equals 3 straight i with hat on top plus 3 straight j with hat on top minus 2 straight k with hat on top
The above three vectors are coplanar
rightwards double arrow AB with rightwards arrow on top. space open parentheses AC with rightwards arrow on top space cross times space AD with rightwards arrow on top close parentheses space equals space 0
rightwards double arrow space open vertical bar table row 1 cell straight x minus 1 end cell cell space space 4 end cell row 1 0 cell negative 3 end cell row 3 3 cell negative 2 end cell end table close vertical bar space equals space 0
rightwards double arrow space 1 left parenthesis 10 plus 9 right parenthesis minus left parenthesis straight x minus 1 right parenthesis space left parenthesis negative 2 plus 9 right parenthesis plus 4 left parenthesis 3 minus 0 right parenthesis space equals space 0
rightwards double arrow 9 minus 7 left parenthesis straight x minus 1 right parenthesis plus 12 space equals 0
rightwards double arrow negative 7 left parenthesis straight x minus 1 right parenthesis space equals space minus 21
rightwards double arrow straight x minus 1 space equals space 3
therefore space space straight x space equals space 4
 
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